Particle manipulation in Hele–Shaw flow with programmable hydrodynamics

This paper presents a microfluidic approach that dynamically controls the hydrodynamic flow and the streamlines to enable complex multi-particle manipulations within a single device. The approach combines the design of a flow-through microfluidic Hele–Shaw flow cell together with an optimization procedure to find a priori optimal particle pathlines, and an effective proportional–integral–derivative (PID) feedback controller to provide real-time control over the particle manipulations. In the device, particles are manipulated with hydrodynamic forces, by using a uniform flow through the flow cell and three inlets perpendicular to the flow cell. The streamlines within the device are manipulated by injecting or extracting fluid through the three inlets. The Hele–Shaw geometry allows a fast and accurate prediction of the particle trajectory, meaning only a simple PID controller is required to correct for particle deviations. The robustness of this approach is demonstrated by implementing multiple functions within the device, including particle trapping, particle sorting, particle separation, and assembly. The real-time control procedure affords accurate particle manipulation, with a maximum error on the order of the diameter of the particle.